Manufacturing, Mathematic Models and Meshing Analysis for the Cycloid Grooves of the Cycloid Ball Planetary Drive

Based on the space meshing theory, this paper proposes mathematic models for the cycloid grooves on central disc and planetary disc of the cycloid ball planetary drive generated by cone milling cutter. The meshing equations are established, and the surfaces equations of the epitrochoid and hypotrochoid enclosed grooves are deduced. The formulae of the undercutting limit points, the principal curvatures and the principal directions are also derived. Based on the proposed mathematic models, the effects of variation in manufacturing depth for the cycloid grooves on the undercutting are analyzed through a numerical example, and maximum manufacturing depth of non-undercutting is derived. Then, the simulation figures of cycloid grooves are drawn and the curves of the principal curvatures are described. These results offers theoretical basis for manufacturing of the cycloid grooves.